Since you already know that you shouldn't rely on this information unless absolutely necessary, here it comes. My general observation across various toolchains (MSVC, gcc/ld, clang/llvm, etc) is that the order in which your object files are passed to the linker is the order in which they will be initialized.
There are exceptions to this, and I do not claim to all of them, but here are the ones I ran into myself:
1) GCC versions prior to 4.7 actually initialize in the reverse order of the link line. This ticket in GCC is when the change happened, and it broke a lot of programs that depended on initialization order (including mine!).
2) In GCC and Clang, usage of constructor function priority can alter the initialization order. Note that this only applies to functions that are declared to be "constructors" (i.e. they should be run just like a global object constructor would be). I have tried using priorities like this and found that even with highest priority on a constructor function, all constructors without priority (e.g. normal global objects, constructor functions without priority) will be initialized first. In other words, the priority is only relative to other functions with priorities, but the real first class citizens are those without priority. To make it worse, this rule is effectively the opposite in GCC prior to 4.7 due to point (1) above.
3) On Windows, there is a very neat and useful shared-library (DLL) entry-point function called DllMain(), which if defined, will run with parameter "fdwReason" equal to DLL_PROCESS_ATTACH directly after all global data has been initialized and before the consuming application has a chance to call any functions on the DLL. This is extremely useful in some cases, and there absolutely is not analogous behavior to this on other platforms with GCC or Clang with C or C++. The closest you will find is making a constructor function with priority (see above point (2)), which absolutely is not the same thing and won't work for many of the use cases that DllMain() works for.
4) If you are using CMake to generate your build systems, which I often do, I have found that the order of the input source files will be the order of their resultant object files given to the linker. However, often times your application/DLL is also linking in other libraries, in which case those libraries will be on the link line after your input source files. If you are looking to have one of your global objects be the very first one to initialize, then you are in luck and your can put the source file containing that object to be the first in the list of source files. However, if you are looking to have one be the very last one to initialize (which can effectively replicate DllMain() behavior!) then you can make a call to add_library() with that one source file to produce a static library, and add the resulting static library as the very last link dependency in your target_link_libraries() call for your application/DLL. Be wary that your global object may get optimized out in this case and you can use the --whole-archive flag to force the linker not to remove unused symbols for that specific tiny archive file.
Closing Tip
To absolutely know the resulting initialization order of your linked application/shared-library, pass --print-map to ld linker and grep for .init_array (or in GCC prior to 4.7, grep for .ctors). Every global constructor will be printed in the order that it will get initialized, and remember that the order is opposite in GCC prior to 4.7 (see point (1) above).
The motivating factor for writing this answer is that I needed to know this information, had no other choice but to rely on initialization order, and found only sparse bits of this information throughout other SO posts and internet forums. Most of it was learned through much experimentation, and I hope that this saves some people the time of doing that!